How to think about… Fields

By Richard Webb

(Image&colon; Shutterstock)

Frank Close has a question. “If you step off the top of a cliff, how does the Earth down there ‘know’ you are up there for it to attract you?” It’s a question that has taxed many illustrious minds before him. Newton’s law of gravitation first allowed such apparently instantaneous “action at a distance”, but he himself was not a fan, describing it in a letter as “so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it”.

Today we ascribe such absurdities to fields. “The idea of some physical mediation – a field of influence – is more satisfying,” says Close, a physicist at the University of Oxford. Earth’s gravitational field, for example, extends out into space in all directions, tugging at smaller objects like the moon and us on top of a cliff; the Earth itself is under the spell of the sun’s gravitational field.

But hang on&colon; what exactly is a field?

On one level, it is just a map. “Ultimately, a field is something that depends on position,” says Frank Wilczek, a theoretical physicist at the Massachusetts Institute of Technology. A gravitational field tells us the strength of gravity at different points in space. Temperatures or isobars on a weather chart are a field. A field is a mathematical abstraction – numbers spread over space.

But there is more to it than that. Witness what physicist Michael Faraday saw in the 19th century, and many a schoolkid has since&colon; iron filings neatly ordering themselves along the lines of a magnetic field, …

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